Technical Field
Embodiments of the subject matter disclosed herein generally relate to survey data processing, more particularly, to obtaining an image of an explored subsurface structure by minimizing differences between observed data and simulated data generated using a velocity model of the structure, with the velocity model iteratively enhanced while preserving amplitude in a selected data-acquisition-related domain.
Discussion of the Background
Seismic exploration of subsurface geophysical structures is customarily used to locate and monitor oil and gas reservoirs. Reflections of seismic waves traveling through the explored subsurface formation are detected by sensors (also known as “receivers”) that record seismic signal versus time values, known as seismic data. Seismic data is processed to identify locations of layer interfaces crossed by the detected waves and the nature of the explored formation's layers, yielding a profile (image) of the formation. This type of seismic exploration is used for formations under land areas and under water bottom surfaces.
FIG. 1 illustrates a marine seismic data acquisition system 100. In this vertical view, a vessel 110 tows seismic sources 112a and 112b and a streamer 114 at predetermined depths under the water surface 111. Although only one streamer is visible in this vertical view, plural streamers are typically spread in a three dimensional volume. Streamer 114, which has a tail buoy 118 and likely other positioning devices attached, houses receivers/sensors 116.
The seismic sources generate seismic waves such as 120a and 120b that propagate through the water layer 30 toward the seafloor 32. At interfaces (e.g., 32 and 36) between layers (e.g., water layer 30, first layer 34, and second layer 38) inside which the seismic waves propagate with different wave propagation velocity, the waves' propagation directions change as the waves are reflected and/or transmitted/refracted/diffracted. Seismic waves 120a and 120b are partially reflected as 122a and 122b and partially transmitted as 124a and 124b at seafloor 32. Transmitted waves 124a and 124b travel through first layer 34, are then reflected as waves 126a and 126b, and transmitted as 128a and 128b at interface 36. At the surface of reservoir 40, waves 128a and 128b are then partially transmitted as waves 130a and 130b and partially reflected as waves 132a and 132b. The waves traveling upward may be detected by receivers 116. Maxima and minima in the amplitude versus time data recorded by receivers carry information about the interfaces and traveling time through layers.
Seismic data analysis is complex because the recorded data is the result of interrelated physical processes and noise. Velocity models of the explored formation, which are representations of wave propagation velocity inside the formation, are often employed to simulate the acquired data. Reflected real or simulated data may be migrated in time or depth (i.e., re-localized at their positions parameterized in depth or in vertical time) using the formation's velocity model. Here the term “underground” refers not only to formations under land areas, but also to formations under the ocean floor. The velocity model may also take into consideration the different velocities through different ocean water layers due to currents, temperature, etc. If the layers are more or less homogenous, the velocity model is relatively simple. However, in reality, significant geophysical features must be considered. Such features include anisotropic velocity variations, complex geological formations such as salt and basalt structures, heavily faulted zones, anisotropic environments due to sedimentation or fracturing, over-thrusts, shallow gas, etc. Velocity may also depend on the type of rock and depth, since rocks under pressure tend to have higher velocity.
Full waveform inversion (FWI) has been an important tool in building and improving velocity models (see, e.g., A. Tarantola's 1984 article, “Inversion of Seismic Reflection Data in the Acoustic Approximation,” in Geophysics, 49, pages 1259-1266, the content of which is incorporated herein in its entirety). Classical FWI methods involve minimization of a square misfit (also known as “cost”) function between the calculated (i.e., modeled) data and observed (real, acquired) data. The connection between migration and the gradient of FWI was identified early in FWI's history (see, e.g., P. Lailly's 1983 article, “The seismic inverse problem as a sequence of before stack migrations,” in the Conference on Inverse Scattering, Theory and application, SIAM, Philadelphia, Pa., USA, Expanded Abstracts, pages 206-220, the content of which is incorporated herein in its entirety). Practically migration and gradient of FWI (used in the local non-linear optimization process) both involve the zero time lag cross-correlation of the propagated incident wavefield by the back-propagated reflected wavefield. This connection is valid for reflected waves, but not for diving waves. Indeed, while diving waves are generally muted in depth migration, they are critical to FWI's success (see, e.g., R. G. Pratt's 1999 article, “Seismic waveform inversion in the frequency domain, Part1: Theory and verification in a physical scale model,” in Geophysics, 64, pages 888-901, the content of which is incorporated herein in its entirety). This difference, in addition to the non-linear aspect of FWI, implies that FWI is not fully equivalent to a migration plus a stratigraphic inversion. However, some interesting cross-fertilizations between these techniques are present.
It is desirable to improve FWI methods for obtaining high-resolution velocity models from reflected waves in a more reliable and faster manner than conventional FWI.